CN110417047B - Method for analyzing SSCI damping characteristics of doubly-fed fan based on complex torque coefficient - Google Patents
Method for analyzing SSCI damping characteristics of doubly-fed fan based on complex torque coefficient Download PDFInfo
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Abstract
The invention relates to a method for analyzing the SSCI damping characteristic of a double-fed fan based on a complex torque coefficient. On the basis, the influence of different control parameters of wind speed, series compensation degree, rotating speed and RSC on the SSCI stability characteristic is analyzed by using an electric damping coefficient expression of electromagnetic torque. The analysis result shows that: decreasing wind speed, increasing the degree of cross-compensation, increasing the speed of rotation, and proportional and integral parameters of the RSC control all contribute to instability of the SSCI system. And finally, verifying the accuracy and the effectiveness of the SSCI stability of the electrical damping characteristic analysis system by using PSCAD/EMTDC time domain simulation.
Description
Technical Field
The invention relates to a method for analyzing grid-connected stability of a double-fed fan, in particular to a method for analyzing the interaction stability of sub-synchronous control of the double-fed fan connected through a series compensation circuit by using a complex torque coefficient method.
Background
With the maturity of wind power generation technology and the reduction of production cost, clean and renewable wind power generation is rapidly developed under the support of national policy. A double-fed induction generator (DFIG) is one of the main variable speed wind power generators currently used because it can realize efficient and low-cost power generation and flexible active and reactive decoupling control. Meanwhile, the compensation series capacitor of the power transmission line can reduce line loss, improve power transmission capacity and system stability, has good power transmission economy, and is a main measure for large-scale wind power transmission. However, a series compensation capacitor in the power transmission line may cause Sub-synchronous resonance (SSR) of the DFIG wind power plant, and further cause the wind driven generator to quit operation and damage the crowbar circuit, which finally affects the safe and stable operation of the large-scale wind power and delivery system.
The Sub-synchronous resonance of the wind power field of the DFIG mainly comprises Induction Generator Effect (IGE), sub-synchronous control interaction (SSCI) and Sub-synchronous torsional vibration interaction (SSTI). Because the rigidity coefficient of a wind turbine shafting is much smaller than that of a synchronous generator, the SSTI can be caused only when a line needs to exceed the actually-allowed series compensation degree, and the SSTI basically cannot occur in a double-fed wind turbine wind power plant. The IGE is mainly caused by the interaction between a doubly-fed generator and a series compensation capacitor on a transmission line; and the SSCI is mainly related to the controller parameters of the wind turbine and the series compensation capacitor of the transmission line.
At present, both domestic and foreign researches mainly adopt a characteristic value analysis and participation factor analysis method, a time domain simulation method, an impedance analysis method, a frequency scanning method and a transfer function analysis method to analyze SSCI (steady state simulation) caused by grid connection of a series compensation circuit of a DFIG (doubly-fed induction generator) wind power plant, and research results show that strong correlation exists between the SSCI of the grid connection of the doubly-fed wind generator and wind speed, series compensation and Rotor Side Converter (RSC) inner loop proportion parameters, but the influence of RSC inner loop integral coefficients and outer loop PI parameters on the SSCI of the doubly-fed wind generator is rarely considered. Actually, the RSC outer loop PI parameter and the inner loop integral coefficient have certain influence on the SSCI of the doubly-fed fan grid-connected system, so that the influence of the RSC controller parameter on the SSCI stability of the doubly-fed fan grid-connected system needs to be researched from a more comprehensive angle. In addition, the rotating speed of the doubly-fed wind turbine is controlled to track the optimal rotating speed of the maximum wind power operation by adjusting the rotating speed of the unit so as to capture the maximum wind energy of the current wind speed, the active power reference value of the stator output by the control is used as the reference input of RSC outer loop control, and the influence of the control dynamic characteristic on the SSCI stability is worthy of deep research.
Disclosure of Invention
The invention mainly solves the technical problems existing in the prior art; the method is used for analyzing the electromagnetic torque electrical damping characteristic of the grid-connected SSCI stability of the doubly-fed wind turbine generator based on a complex torque coefficient method.
It is a further object of the present invention to solve the technical problems of the prior art; the method for analyzing the influence of the wind speed, the series compensation degree, the rotating speed and the RSC controller parameters on the stability of the double-fed wind turbine generator system connected with the grid SSCI through the series compensation circuit based on the electric damping characteristic expression of the electromagnetic torque is provided.
The technical problem of the invention is mainly solved by the following technical scheme:
the method for analyzing the SSCI damping characteristic of the doubly-fed fan based on the complex torque coefficient is characterized by comprising the following steps of:
step 1.1, obtaining an equation of rotor voltage of the doubly-fed wind turbine relative to rotor current according to a rotor voltage equation and a flux linkage equation of the generator as follows:
in the formula (1), u rq ，u rd Voltage components of a rotor q axis and a rotor d axis under a synchronous rotation coordinate system are respectively; i all right angle rq ，i rd Respectively a rotor q-axis current component and a rotor d-axis current component under a synchronous rotating coordinate system; psi s A motor stator flux linkage is issued for a synchronous rotation coordinate system; r is r Respectively, rotor winding resistances; omega 1 、ω r Synchronous rotation angular velocity and rotor rotation angular velocity, respectively; l is s ，L r ，L m Self inductance and mutual inductance of the stator winding and the rotor winding are respectively obtained; p is a differential operator;
step 1.2, according to the RSC current inner loop control block diagram of the doubly-fed fan, the RSC current inner loop control method can obtain the RSC current inner loop control block diagram:
in the formula (2), i re_ref ，i rd_ref Respectively are reference instruction values for RSC current inner loop control of the double-fed fan; k is a radical of formula p3 ，k i3 Proportional coefficients and integral coefficients controlled by the current inner loop of the double-fed fan are respectively; s represents a differential element;
step 1.3, the expression that the rotor current changes along with the reference value can be obtained by combining the vertical formula (1) and the formula (2) as follows:
in the formula (4), phi sq ，ψ sd Respectively a stator q-axis flux linkage component and a stator d-axis flux linkage component under a synchronous rotating coordinate system; u. of sq ，u sd The voltage components of a q axis and a d axis of the stator under a synchronous rotation coordinate system are respectively; i.e. i sq ，i sd The current components of a q axis and a d axis of the stator under a synchronous rotating coordinate system are respectively; psi s And U s Respectively issuing a generator stator flux linkage and a stator machine end voltage in a synchronous rotation coordinate system; by linearizing the formula (4), the stator active power increment of the doubly-fed wind turbine can be further obtained as follows:
in the formula (5), Δ P s Representing the active power increment of the stator; Δ i sd ，Δi sd Representing stator current d-axis and q-axis increments; Δ i rq Represents rotor current q-axis delta;
step 1.5, on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring of the RSC of the doubly-fed fan, combining the formula (3) and the formula (5), a block diagram of an active power control system of a stator of the doubly-fed fan can be obtained, and according to the block diagram of the closed-loop control system, a transfer function of the active power of the stator of the doubly-fed fan along with the change of an active power reference value of the RSC stator can be obtained as follows:
in the formula (6), Δ P s_ref Representing the increment of the active power reference value of the stator; k is a radical of formula p2 ，k i2 Respectively representing the proportional coefficient and the integral coefficient of RSC power outer loop control;
step 2, establishing a transfer function of the rotating speed control and RSC control of the doubly-fed wind turbine, specifically, in a maximum wind power tracking mode, carrying out linearization processing on a quadratic fitting polynomial of a reference rotating speed about the active power of the stator and an expression of a stator active power reference value output by the rotating speed control along with the change of the rotating speed of the rotor at a balance point, and then substituting the quadratic fitting polynomial into the transfer function expression of the active power of the RSC stator along with the change of the active power reference value of the RSC stator obtained in the step 1 to obtain the transfer function of the active power of the stator of the doubly-fed wind turbine along with the change of the rotating speed, wherein the transfer function specifically comprises the following steps:
step 2.1, the active power reference value and the maximum wind power operation curve of the stator are as follows:
in the formula (7), ω r_ref A reference command value indicating rotational speed control; p s ，P s_ref Respectively representing the active power and the command value of the active power of the stator; k is a radical of p1 ，k i1 Respectively representing the proportional and integral coefficients of the rotation speed control;
step 2.2, linearizing the equation (7) at the equilibrium point to obtain:
in the formula (8), P s0 A steady state value representing active power of the stator; omega r0 ，ω r_ref0 Steady state values representing a steady state value of the rotor speed and a reference value of the speed, respectively;
step 2.3, substituting the formula (6) and the formula (8) on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring controlled by the RSC of the doubly-fed fan to obtain a control system block diagram of the active power of the stator of the doubly-fed fan along with the change of the rotating speed of the rotor; according to the control block diagram of the closed-loop system, the transfer function of the active power of the stator of the doubly-fed fan along with the change of the rotating speed can be obtained as follows:
step 3, establishing an electric damping characteristic calculation function of the electromagnetic torque of the doubly-fed fan, specifically substituting an approximate relation existing between the active power and the electromagnetic torque of the stator of the doubly-fed fan into the transfer function of the active power of the stator of the doubly-fed fan changing along with the rotating speed obtained in the step 2, and obtaining the transfer function of the electromagnetic torque of the doubly-fed fan changing along with the rotating speed; combining a complex torque coefficient method to obtain an electrical damping characteristic calculation expression of the electromagnetic torque of the doubly-fed fan, and analyzing and judging the stability of the grid-connected SSCI of the doubly-fed fan, wherein the electrical damping characteristic calculation expression specifically comprises the following steps:
step 3.1, the following approximate relation exists between the active power and the electromagnetic torque of the doubly-fed wind turbine stator:
T e ≈n p P s /ω 1 (10)
in the formula (10), n p Is the pole pair number, omega, of the doubly-fed fan 1 Synchronizing the rotation speed of the stator; substituting the formula (12) into the formula (11) can obtain the following transfer function of the electromagnetic torque variation of the doubly-fed fan along with the rotation speed disturbance variation:
step 3.2, when the doubly-fed wind turbine is subjected to series compensation and grid connection, the angular frequency is omega due to disturbance on the steady-state rotating speed of the rotor of the system er Amount of change Δ ω in rotational speed r Electromagnetic torque responding to the rotation speedReal part of gain Re [ G ] of disturbance component Te (jω er )]The electric damping torque coefficient of the complex torque is obtained;
step 3.3, considering that the mechanical damping value of the wind turbine generator is small, the relative electric damping torque coefficient is Re G Te (jω er )]The stability of the system SSCI is analyzed directly through the electrical damping torque coefficient of the doubly-fed wind turbine generator through a series compensation grid-connected system because the mechanical damping influence of the wind turbine generator is ignored; when Re [ G ] Te (jω er )]>When the damping value is 0, the electrical damping of the system to the disturbance component is positive, and after SSCI disturbance occurs, the oscillation can be gradually attenuated and tends to be stable; when Re [ G ] Te (jω er )]<When the voltage is 0, the electrical damping provided by the system for SSCI disturbance is negative, so that subsynchronous oscillation gradually diverges and the system oscillation is unstable; when Re [ G ] Te (jω er )]When the angular frequency is not less than 0, the electrical damping provided by the system for the SSCI disturbance is zero, the electromagnetic torque of the doubly-fed fan can generate continuous constant-amplitude oscillation, and the angular frequency of the rotating speed disturbance component is called as critical stable angular frequency omega at the moment er0 ；
step 4.1, setting a proportional coefficient k of rotation speed control p1 And integral coefficient k i1 0.5 and 5, respectively, the proportionality coefficient k of the outer loop power control p2 And integral coefficient k i2 0.3 and 5 respectively, and the proportionality coefficient k of RSC inner ring current control of the doubly-fed fan p3 And integral coefficient k i3 0.2 and 5, respectively; series compensation power transmission network with wind speed of 10m/sThe crosstalk compensation degree of (2) is 40%;
step 4.2, setting the wind speeds of the double-fed wind turbine generator set to be 8m/s,10m/s and 12m/s respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator set at different wind speeds is observed;
step 4.3, setting the series compensation degrees of the series compensation power transmission network to be 25%,40% and 60%, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator is observed under different series compensation degrees;
step 4.4, setting the proportional coefficients of the rotating speed control to be 0.1,0.5 and 1 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator under different rotating speed control proportionality coefficients is observed;
step 4.5, setting integral coefficients of the rotation speed control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different rotating speed control integral coefficients is observed;
step 4.6, setting the ratio coefficients of RSC outer loop power control to be 0.2,0.3 and 0.4 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC outer ring power control proportionality coefficients is observed;
step 4.7, setting the integral coefficients of RSC outer loop power control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different integral coefficients controlled by RSC outer ring power is observed;
step 4.8, setting the ratio coefficients of RSC inner ring current control to be 0.15,0.2 and 0.25 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC inner loop current control proportionality coefficients is observed;
step 4.9, setting the integral coefficients of RSC inner loop current control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC inner ring current control integral coefficients is observed.
Therefore, the invention has the following advantages: 1. the electric damping of the doubly-fed wind turbine through the series compensation grid-connected system can be specifically quantized, and whether the system is stable after being disturbed and whether SSCI occurs can be judged based on the electric damping obtained through calculation; 2. through analyzing the influence of the wind speed, the series compensation degree, the rotating speed control and the RSC control parameters on the electrical damping characteristic of the doubly-fed fan through the series compensation grid-connected system, the research shows that the higher the wind speed is, the larger the electrical damping of the system is, the better the stability of the system is, along with the increase of the series compensation degree, the higher the oscillation frequency is, the electrical damping of the system is gradually reduced from positive damping to negative damping, and the system is gradually changed from an oscillation convergence stable state to an oscillation divergence state; 3. the larger the proportional coefficient and the integral coefficient of the rotating speed control and the RSC control are, the smaller the system electrical damping is, the worse the stability is, the smaller the influence of the PI parameter of the rotating speed control on the SSCI is, the larger the influence of the PI parameter of the outer ring of the RSC and the integral coefficient of the inner ring of the RSC on the SSCI is, and the largest influence of the proportional coefficient of the inner ring of the RSC on the SSCI is.
Drawings
FIG. 1 is an equivalent model of a doubly-fed wind turbine wind power plant merged into an infinite power grid through a series compensation power transmission line.
Fig. 2 is a double-layer cascade control structure of power outer loop and current inner loop control of double-fed fan RSC control.
Fig. 3 is a block diagram of a control system for changing the active power of a stator of the doubly-fed wind turbine along with a reference value of the stator of the doubly-fed wind turbine.
FIG. 4 is a block diagram of a doubly-fed wind turbine speed control system.
FIG. 5 is a control system block diagram of the active power of a stator of the doubly-fed wind turbine changing with the rotating speed of a rotor.
FIG. 6 is an active power oscillation curve of a series compensation capacitor of an access line of a doubly-fed wind power plant at different wind speeds.
FIG. 7 is an active power oscillation curve of a series compensation capacitor of an access line of a doubly-fed wind power plant under different line series compensation degrees.
FIG. 8 is an active power oscillation curve of a series compensation capacitor of an access line of a doubly-fed wind farm under different proportional coefficients of rotation speed control.
FIG. 9 is an active power oscillation curve of a series compensation capacitor of an access circuit of a doubly-fed wind power plant under different integral coefficients of rotation speed control.
FIG. 10 is an active power oscillation curve of series compensation capacitors of a double-fed wind power plant access line under different scaling factors of RSC outer loop power control.
FIG. 11 is an active power oscillation curve of a series compensation capacitor of a double-fed wind power plant access line under different integration coefficients of RSC outer loop power control.
FIG. 12 is an active power oscillation curve of a series compensation capacitor of an access line of a doubly-fed wind power plant under different RSC inner loop current control proportionality coefficients.
FIG. 13 is an active power oscillation curve of a series compensation capacitor of a double-fed wind power plant access line under different RSC inner loop current control integral coefficients.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b):
1. firstly, the method principle of the invention is introduced, which mainly comprises the following steps:
step 2, establishing a transfer function of the rotating speed control and RSC control of the doubly-fed fan: in a maximum wind power tracking mode, carrying out linearization processing on a quadratic fitting polynomial of the reference rotating speed about the stator active power and an expression of a stator active power reference value output by rotating speed control along with the change of the rotor rotating speed at a balance point, and then substituting the expression into the transfer function expression of the RSC stator active power along with the change of the reference value obtained in the step 1 to obtain a transfer function of the doubly-fed fan stator active power along with the change of the rotating speed;
step 3, calculating to obtain an electrical damping characteristic expression of the electromagnetic torque of the doubly-fed fan: and (3) substituting the approximate relation between the active power and the electromagnetic torque of the stator of the double-fed fan into the transfer function of the active power of the stator of the double-fed fan changing along with the rotating speed obtained in the step (2) to obtain the transfer function of the electromagnetic torque of the double-fed fan changing along with the rotating speed. Combining a complex torque coefficient method to obtain an electrical damping characteristic calculation expression of the electromagnetic torque of the doubly-fed fan, and analyzing and judging the stability of the grid-connected SSCI of the doubly-fed fan, wherein the complex torque coefficient method is adopted according to the following principle: the complex torque coefficient method is a method for determining whether a system is stable at a sub-synchronous frequency according to the sum of a mechanical damping coefficient and an electrical damping coefficient of a generator, and is generally used for analyzing the sub-synchronous oscillation of the system. Under power angle disturbance with a frequency λ, the electromagnetic torque increment of the generator can be expressed as:
in the formula (1), delta and delta omega are respectively the power angle increment and the angular speed increment of the generator, K e And D e Electrical synchronous torque coefficients and electrical damping torque coefficients, respectively. It can be obtained from formula (1):
ΔT e /Δω＝D e (λ)-jK e (λ)/λ (2)
according to the electric damping torque coefficient D in the formula (2) e (lambda) and the mechanical damping D of the generator itself m If the generator has D under power angle disturbance with frequency of lambda e (λ)+D m <0, the generator will produce subsynchronous oscillation, and the system is in an unstable state.
And 4, establishing an equivalent doubly-fed wind power plant grid-connected system simulation model through series compensation lines in the PSCAD/EMTDC. The wind power plant is composed of 100 2MW double-fed fans, each double-fed fan is connected to a unified public bus through a 0.69/35kV transformer T1, and parameters and operation conditions of all the fans are the same. The whole wind power plant is connected to a 220kV power transmission line through a 35kV/220kV booster transformer T2, and then is connected to a 500kV long-distance power transmission line through a 220kV/500kV booster transformer T3 to be merged into an infinite power grid. Under the condition of ensuring the change of a single parameter, the stability of the doubly-fed wind turbine generator system through a series compensation grid-connected system under different operation conditions is observed by setting different parameters.
2. The method of the present invention is specifically described below with reference to specific examples, which mainly comprise the following steps:
step 1.1, obtaining an equation of rotor voltage of the doubly-fed wind turbine relative to rotor current according to a rotor voltage equation and a flux linkage equation of the generator as follows:
in the formula (3), u rq ，u rd Voltage components of a rotor q axis and a rotor d axis under a synchronous rotation coordinate system are respectively; i.e. i rq ，i rd Respectively a rotor q-axis current component and a rotor d-axis current component under a synchronous rotating coordinate system; psi s A motor stator flux linkage is issued for a synchronous rotation coordinate system; r is r Respectively, rotor winding resistances; omega 1 、ω r Synchronous rotational angular velocity and rotor rotational angular velocity, respectively; l is s ，L r ，L m Self inductance and mutual inductance of the stator winding and the rotor winding are respectively obtained; p is a differential operator.
Step 1.2, according to the RSC current inner loop control block diagram of the doubly-fed fan, the RSC current inner loop control method can obtain the RSC current inner loop control block diagram:
in the formula (4), i re_ref ，i rd_ref Respectively are reference instruction values for RSC current inner loop control of the double-fed fan; k is a radical of p3 ，k i3 Proportional coefficient and integral coefficient of the double-fed fan current inner loop control are respectively; s represents a differential element.
Step 1.3, the expression of the rotor current changing along with the reference value can be obtained by combining the vertical type (3) and the formula (4) as follows:
in the formula (6), ψ sq ，ψ sd Respectively a stator q-axis flux linkage component and a stator d-axis flux linkage component under a synchronous rotating coordinate system; u. u sq ，u sd Are respectively synchronousRotating q-axis and d-axis voltage components of the stator under a coordinate system; i.e. i sq ，i sd The current components of a stator q axis and a stator d axis under a synchronous rotating coordinate system are respectively; psi s And U s The synchronous rotating coordinate system sends a stator flux linkage of the generator and the stator machine end voltage respectively. By linearizing the equation (6), the stator active power increment of the doubly-fed wind turbine can be further obtained as follows:
in the formula (7), Δ P s Representing the active power increment of the stator; Δ i sd ，Δi sd Representing stator current d-axis and q-axis increments; Δ i rq Representing the rotor current q-axis delta.
Step 1.5, on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring controlled by the RSC of the doubly-fed fan, a block diagram of a stator active power control system of the doubly-fed fan can be obtained by combining the formula (5) and the formula (7), and according to the block diagram of the closed-loop control system, a transfer function of the stator active power of the doubly-fed fan along with the change of the RSC stator active power reference value can be obtained as follows:
in the formula (8), Δ P s_ref Representing the increment of the active power reference value of the stator; k is a radical of p2 ，k i2 Respectively representing the proportional and integral coefficients of the RSC power outer loop control.
And 2, in a maximum wind power tracking mode, carrying out linearization processing on a quadratic fitting polynomial of the reference rotating speed about the stator active power and an expression of the stator active power reference value output by rotating speed control along with the change of the rotating speed at a balance point, and then substituting the quadratic fitting polynomial into the transfer function expression of the stator active power obtained in the step 1 along with the change of the RSC stator active power reference value to obtain a transfer function of the active power of the stator of the doubly-fed fan along with the change of the rotating speed. The process of specifically solving the transfer function of the active power of the stator of the doubly-fed fan along with the change of the rotating speed is as follows:
step 2.1, according to the block diagram of the double-fed fan rotating speed control system, the following active power reference value and maximum wind power operation curve of the stator can be obtained:
in the formula (9), ω r_ref A reference command value indicating rotational speed control; p s ，P s_ref Respectively representing the active power and the command value of the active power of the stator; k is a radical of p1 ，k i1 Respectively representing the proportional and integral coefficients of the speed control.
Step 2.2, the formula (9) is linearized at the equilibrium point, and the following can be obtained:
in the formula (10), P s0 A steady state value representing active power of the stator; omega r0 ，ω r_ref0 Representing steady state values of the rotor speed and the speed reference, respectively.
And 2.3, substituting the formula (8) and the formula (10) on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring controlled by the RSC of the doubly-fed fan to obtain a control system block diagram of the active power of the stator of the doubly-fed fan changing along with the rotating speed of the rotor. According to the control block diagram of the closed-loop system, the transfer function of the active power of the stator of the doubly-fed fan along with the change of the rotating speed can be obtained as follows:
and 3, substituting the approximate relation between the active power and the electromagnetic torque of the stator of the doubly-fed fan into the transfer function of the active power of the stator of the doubly-fed fan changing along with the rotating speed to obtain the transfer function of the electromagnetic torque of the doubly-fed fan changing along with the rotating speed. And (3) combining a complex torque coefficient method to obtain an electrical damping characteristic calculation expression of the electromagnetic torque of the double-fed fan, and analyzing and judging the stability of the grid-connected SSCI of the double-fed fan. Specifically, the process of obtaining the electrical damping characteristic expression of the doubly-fed wind turbine is as follows:
step 3.1, the following approximate relation exists between the active power and the electromagnetic torque of the doubly-fed fan stator:
T e ≈n p P s /ω 1 (12)
in the formula (12), n p Is the pole pair number, omega, of the doubly-fed fan 1 The stator synchronous speed is obtained. Substituting the formula (12) into the formula (11) can obtain the following transfer function of the electromagnetic torque variation of the doubly-fed fan along with the rotation speed disturbance variation:
step 3.2, combining the formula (2) and the formula (13), namely, when the doubly-fed wind turbine is subjected to series compensation grid-connected system, the angular frequency is omega caused by disturbance on the steady-state rotating speed of a rotor er Amount of change in rotational speed of Δ ω r The real gain part Re G of the electromagnetic torque responding to the rotation speed disturbance component Te (jω er )]I.e. the electrical damping torque coefficient of the complex torque.
Step 3.3, considering that the mechanical damping value of the wind turbine generator is small, the relative electric damping torque coefficient is Re G Te (jω er )]The stability of the SSCI system is analyzed directly through the electrical damping torque coefficient of the doubly-fed wind turbine generator through a series compensation grid-connected system because the mechanical damping influence of the wind turbine generator is ignored. When Re [ G ] Te (jω er )]>When the damping value is 0, the electrical damping of the system to the disturbance component is positive, and after SSCI disturbance occurs, the oscillation can be gradually attenuated and tends to be stable; when Re [ G ] Te (jω er )]<When the voltage is 0, the electrical damping provided by the system for SSCI disturbance is negative, so that subsynchronous oscillation gradually diverges and the system oscillation is unstable; when Re [ G ] Te (jω er )]When the angular frequency of the rotating speed disturbance component is called as critical stable angular frequency omega at the moment, the electrical damping provided by the system for the SSCI disturbance is zero, the constant-amplitude oscillation of the electromagnetic torque of the doubly-fed fan can be generated, and the angular frequency of the rotating speed disturbance component is called as critical stable angular frequency omega at the moment er0 。
And 4, establishing an equivalent doubly-fed wind power plant grid-connected system simulation model through series compensation lines in the PSCAD/EMTDC. The wind power plant is composed of 100 2MW double-fed fans, each double-fed fan is connected to a unified public bus through a 0.69/35kV transformer T1, and parameters and operation conditions of all the fans are the same. The whole wind power plant is connected to a 220kV power transmission line through a 35kV/220kV booster transformer T2, and then is connected to a 500kV long-distance power transmission line through a 220kV/500kV booster transformer T3 to be merged into an infinite power grid. Under the condition of ensuring the change of a single parameter, the stability of the doubly-fed wind turbine generator system through a series compensation grid-connected system under different operation conditions is observed by setting different parameters. The specific simulation experiment steps are as follows:
step 4.1, setting a proportional coefficient k of rotating speed control p1 And integral coefficient k i1 0.5 and 5, respectively, the proportionality coefficient k of the outer loop power control p2 And integral coefficient k i2 0.3 and 5 respectively, and the proportionality coefficient k of RSC inner ring current control of the doubly-fed fan p3 And integral coefficient k i3 0.2 and 5, respectively. The wind speed is set to be 10m/s, and the series compensation degree of the series compensation power transmission network is 40%.
And 4.2, setting the wind speeds of the double-fed wind turbine generator set to be 8m/s,10m/s and 12m/s respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator is observed at different wind speeds.
And 4.3, setting the series compensation degrees of the series compensation power transmission network to be 25%,40% and 60%, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator under different series compensation degrees is observed.
And 4.4, setting the proportional coefficients of the rotating speed control to be 0.1,0.5 and 1 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different rotating speed control proportionality coefficients is observed.
And 4.5, setting the integral coefficients of the rotation speed control to be 1,5 and 10 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different rotating speed control integral coefficients is observed.
And 4.6, setting the ratio coefficients of RSC outer loop power control to be 0.2,0.3 and 0.4 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC outer ring power control proportionality coefficients is observed.
And 4.7, setting the integral coefficients of RSC outer loop power control to be 1,5 and 10 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different integral coefficients controlled by RSC outer ring power is observed.
And 4.8, setting the ratio coefficients of RSC inner ring current control to be 0.15,0.2 and 0.25 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC inner ring current control proportionality coefficients is observed.
And 4.9, setting the integral coefficients of RSC inner ring current control to be 1,5 and 10 respectively, and keeping other parameters unchanged. In the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different integral coefficients controlled by RSC inner ring current is observed.
And 4.10, observing the stability of the series compensation grid-connected system by the double-fed wind turbine generator set under the operation condition with different parameters, wherein the higher the wind speed is, the lower the series compensation degree is, and the system is more easily stabilized after being disturbed. The larger the proportional coefficient and the integral coefficient of the rotating speed control and the RSC control are, the poorer the system stability is, and the system is easier to oscillate and disperse after being disturbed.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (1)
1. The method for analyzing the SSCI damping characteristic of the double-fed fan based on the complex torque coefficient is characterized by comprising the following steps of:
step 1, establishing an RSC control transfer function of the doubly-fed wind turbine, specifically, according to a rotor voltage equation and a flux linkage equation of a generator, combining RSC current inner loop control of the doubly-fed wind turbine, and obtaining a transfer function expression of rotor current changing along with a reference value; meanwhile, on the premise of orientation of a magnetic chain d axis of the generator stator, a transfer function expression of the active power of the doubly-fed fan stator changing along with the RSC stator active power reference value is obtained by combining an expression of the active power of the generator stator, and the expression specifically comprises the following steps:
step 1.1, obtaining an equation of the rotor voltage of the doubly-fed wind turbine relative to the rotor current according to a rotor voltage equation and a flux linkage equation of the generator as follows:
in the formula (1), u rq ，u rd Voltage components of a rotor q axis and a rotor d axis under a synchronous rotation coordinate system are respectively; i.e. i rq ，i rd Respectively a rotor q-axis current component and a rotor d-axis current component under a synchronous rotating coordinate system; psi s A motor stator flux linkage is issued for a synchronous rotation coordinate system; r r Respectively, rotor winding resistances; omega 1 、ω r Synchronous rotational angular velocity and rotor rotational angular velocity, respectively; l is s ，L r ，L m Are respectively fixed,Self-inductance and mutual inductance of the rotor windings; p is a differential operator;
step 1.2, according to the RSC current inner loop control block diagram of the doubly-fed fan, the RSC current inner loop control method can obtain the RSC current inner loop control block diagram:
in the formula (2), i re_ref ，i rd_ref Respectively are reference instruction values for controlling the RSC current inner loop of the doubly-fed fan; k is a radical of p3 ，k i3 Proportional coefficient and integral coefficient of the double-fed fan current inner loop control are respectively; s represents a differential element;
step 1.3, the expression that the rotor current changes along with the reference value can be obtained by combining the vertical formula (1) and the formula (2) as follows:
step 1,4, because the generator adopts stator flux d-axis orientation, the stator flux and voltage equation of the generator is as follows:
in the formula (4), phi sq ，ψ sd Respectively a stator q-axis flux linkage component and a stator d-axis flux linkage component under a synchronous rotating coordinate system; u. of sq ，u sd The voltage components of a q axis and a d axis of the stator under a synchronous rotating coordinate system are respectively; i.e. i sq ，i sd The current components of a q axis and a d axis of the stator under a synchronous rotating coordinate system are respectively; psi s And U s Respectively issuing a stator flux linkage and a stator machine end voltage of a motor in a synchronous rotating coordinate system; by linearizing the formula (4), the stator active power increment of the doubly-fed wind turbine can be further obtained as follows:
in the formula (5), Δ P s Representing the active power increment of the stator; delta i sd ，Δi sd Representing stator current d-axis and q-axis increments; Δ i rq Represents rotor current q-axis delta;
step 1.5, on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring controlled by the RSC of the doubly-fed fan, a block diagram of a stator active power control system of the doubly-fed fan can be obtained by combining the formula (3) and the formula (5), and according to the block diagram of the closed-loop control system, a transfer function of the stator active power of the doubly-fed fan along with the change of the RSC stator active power reference value can be obtained as follows:
in the formula (6), Δ P s_ref Representing the increment of the active power reference value of the stator; k is a radical of p2 ，k i2 Respectively representing the proportional coefficient and the integral coefficient of RSC power outer loop control;
step 2, establishing a transfer function of the rotating speed control and RSC control of the doubly-fed wind turbine, specifically, under a maximum wind power tracking mode, performing linearization processing on a quadratic fitting polynomial of a reference rotating speed about active power of a stator and an expression of a stator active power reference value output by the rotating speed control and changing with the rotating speed of a rotor at a balance point, and then substituting the quadratic fitting polynomial into the transfer function expression of the RSC stator active power obtained in the step 1 and changing with the RSC stator active power reference value to obtain the transfer function of the active power of the stator of the doubly-fed wind turbine changing with the rotating speed, specifically comprising the following steps:
step 2.1, the active power reference value and the maximum wind power operation curve of the stator are as follows:
in the formula (7), ω r_ref A reference command value indicating rotational speed control; p s ，P s_ref Respectively represent the active power of the stator anda command value for work power; k is a radical of p1 ，k i1 Respectively representing the proportional and integral coefficients of the rotation speed control;
step 2.2, the formula (7) is linearized at the equilibrium point, and the following can be obtained:
in the formula (8), P s0 A steady state value representing active power of the stator; omega r0 ，ω r_ref0 Steady state values representing a steady state value of the rotor speed and a reference value of the speed, respectively;
step 2.3, substituting the formula (6) and the formula (8) on the basis of a double-layer cascade control structure controlled by a power outer ring and a current inner ring controlled by the RSC of the doubly-fed fan to obtain a control system block diagram of the active power of the stator of the doubly-fed fan along with the change of the rotating speed of the rotor; according to a control block diagram of a closed loop system, a transfer function of the active power of the stator of the doubly-fed wind turbine along with the change of the rotating speed can be obtained as follows:
step 3, establishing an electric damping characteristic calculation function of the electromagnetic torque of the doubly-fed fan, specifically substituting an approximate relation existing between the active power and the electromagnetic torque of the stator of the doubly-fed fan into the transfer function of the active power of the stator of the doubly-fed fan changing along with the rotating speed obtained in the step 2, and obtaining the transfer function of the electromagnetic torque of the doubly-fed fan changing along with the rotating speed; combining a complex torque coefficient method to obtain an electrical damping characteristic calculation expression of the electromagnetic torque of the doubly-fed fan, and analyzing and judging the stability of the doubly-fed fan grid-connected SSCI, specifically comprising the following steps:
step 3.1, the following approximate relation exists between the active power and the electromagnetic torque of the doubly-fed wind turbine stator:
T e ≈n p P s /ω 1 (10)
in the formula (10), n p Is the pole pair number, omega, of the doubly-fed fan 1 Synchronous rotation speed of the stator; substituting the formula (12) into the formula (11) can obtain the following transfer function of the electromagnetic torque variation of the doubly-fed fan along with the rotation speed disturbance variation:
step 3.2, when the doubly-fed wind turbine is subjected to series compensation and grid connection, the angular frequency is omega due to disturbance on the steady-state rotating speed of the rotor of the system er Amount of change in rotational speed of Δ ω r The real gain part Re G of the electromagnetic torque responding to the rotation speed disturbance component Te (jω er )]The electric damping torque coefficient of the complex torque is obtained;
step 3.3, considering that the mechanical damping value of the wind turbine generator is small, the relative electric damping torque coefficient is Re G Te (jω er )]The stability of the system SSCI is analyzed directly through the electrical damping torque coefficient of the doubly-fed wind turbine generator through a series compensation grid-connected system because the mechanical damping influence of the wind turbine generator is ignored; when Re [ G ] Te (jω er )]>When the damping value is 0, the electrical damping of the system to the disturbance component is positive, and after SSCI disturbance occurs, the oscillation can be gradually attenuated and tends to be stable; when Re [ G ] Te (jω er )]<When the voltage is 0, the electrical damping provided by the system for SSCI disturbance is negative, so that subsynchronous oscillation is gradually dispersed and the system oscillation is unstable; when Re [ G ] Te (jω er )]When the angular frequency is not less than 0, the electrical damping provided by the system for the SSCI disturbance is zero, the electromagnetic torque of the doubly-fed fan can generate continuous constant-amplitude oscillation, and the angular frequency of the rotating speed disturbance component is called as critical stable angular frequency omega at the moment er0 ；
Step 4, establishing an equivalent doubly-fed wind power plant grid-connected system simulation model through series compensation lines in the PSCAD/EMTDC; the wind power plant consists of 100 2MW double-fed fans, each double-fed fan is connected to a unified public bus through a 0.69/35kV transformer T1, and parameters and operation conditions of all the fans are the same; the whole wind power plant is connected to a 220kV power transmission line through a 35kV/220kV booster transformer T2, and then connected to a 500kV long-distance power transmission line through a 220kV/500kV booster transformer T3 to be merged into an infinite power grid; under the condition of ensuring the single parameter change, observing the stability of the doubly-fed wind turbine generator through a series compensation grid-connected system under different operation conditions by setting different parameters; the specific simulation experiment steps are as follows:
step 4.1, setting a proportional coefficient k of rotation speed control p1 And integral coefficient k i1 0.5 and 5, respectively, the proportionality coefficient k of the outer loop power control p2 And integral coefficient k i2 0.3 and 5 respectively, and the proportionality coefficient k of RSC inner ring current control of the doubly-fed fan p3 And integral coefficient k i3 0.2 and 5, respectively; setting the wind speed to be 10m/s and the series compensation degree of the series compensation power transmission network to be 40%;
step 4.2, setting the wind speeds of the double-fed wind turbine generator set to be 8m/s,10m/s and 12m/s respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator at different wind speeds is observed;
step 4.3, setting the series compensation degrees of the series compensation power transmission network to be 25%,40% and 60% respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when a fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the double-fed wind turbine generator under different series compensation degrees is observed;
step 4.4, setting the proportional coefficients of the rotating speed control to be 0.1,0.5 and 1 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different rotating speed control proportionality coefficients is observed;
step 4.5, setting integral coefficients of the rotation speed control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different rotating speed control integral coefficients is observed;
step 4.6, setting the ratio coefficients of RSC outer loop power control to be 0.2,0.3 and 0.4 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC outer ring power control proportionality coefficients is observed;
step 4.7, setting the integral coefficients of RSC outer loop power control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different integral coefficients of RSC outer ring power control is observed;
step 4.8, setting the ratio coefficients of RSC inner ring current control to be 0.15,0.2 and 0.25 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC inner loop current control proportionality coefficients is observed;
step 4.9, setting integral coefficients of RSC inner loop current control to be 1,5 and 10 respectively, and keeping other parameters unchanged; in the simulation process, the initial bypass operation state is changed into online operation when the fixed series compensation capacitor is set for 15s, and the stability of the active power of the output stator of the doubly-fed wind turbine generator under different RSC inner ring current control integral coefficients is observed.
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